Yes, your calculations should have shown you had 18000 false positives from the first screen, screening those at 99% specificity would mean 17820 of them would be correctly identified as true negatives, with only 180 false positives.
If test two was used on its own it would have identified 99900 true positives (vs 98901 in two step, 99 more), but also would have had 90,000 false positives (vs 180 in two step).
Using test two on its on would have cost £10,000,000, using two-step would have cost £2,170,000
Based on screening 1,000,000 people
|Incidence||2 step cases missed||2-step false +ve||2 step cost||test 2 only cases missed||test 2 only false +ve||test 2 only cost||test 1 cases missed||test 1 only false +ve||test 1 only cost|
Final question… At what incidence level would you consider switching from the 2 step system to either of the single tests?